the files that sdt saves go in (about) the same location whether you are loading it using an internet browser from the website, loading it using an internet browser from your computer, or loading it using the flash projector from your computer.
they all save in appdata .. macromedia .. blah blah
the important note is that your internet browser may 'clean up' this folder depending on the settings of the browser.
(the flash data is shared between all browsers, so any of them you use may delete them)
i use firefox quite often, and i usually delete all local content when closing the browser. i installed an addon called selectivecookiedelete
to delete only the cookies and not the flash app data. this was quite a while ago, so i am unsure if the current firefox still includes flash data under its 'cookies' checkbox for 'settings for clearing history'.
my preference is to keep a copy of sdt on my harddrive, and use the flash projector to play it in a convenient window.